Security constrained unit commitment pricing optimization using linear programming for electricity markets

ABSTRACT

The present invention is a method for optimizing security constrained unit commitment in the day ahead wholesale electricity market using mixed integer linear programming techniques. The wholesale electricity market uniquely requires the submission of offers to supply energy and ancillary services at stated prices, as well as bids to purchase energy, and known operating and security constraints. The present invention address the above noted needs by providing a SCUC engine to support and implement the requirements via a computer system implementation.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation-in-part of U.S. patentapplication Ser. No. 10/385,011 filed on Mar. 10, 2003, which is hereinincorporated by reference.

TECHNICAL FIELD

[0002] This invention relates generally to the optimization managementof wholesale electricity markets. In particular, the invention pertainsto the optimization of security constrained unit commitment in regionalwholesale day ahead energy markets.

BACKGROUND ART

[0003] This invention relates generally to a method of determining theoptimal commitments of energy and ancillary services for wholesaleenergy market clearing and pricing. In particular, the inventionpertains to the optimal selection of offers submitted by marketparticipants to satisfy energy and ancillary service requirements forregional electricity markets while satisfying operating and securityconstraints. It may be used by electricity market operators such asRegional Transmission Organizations, Independent System Operators, andIndependent Transmission Providers. It may also be used by marketparticipants as a tool to study various possible bidding strategies andto simulate possible market results.

[0004] A brief description of how electricity markets function under theFederal Energy Regulatory Commission (“FERC”) regulations may be helpfulin understanding the field of the present invention. In April 1996, FERCOrder 888, “Promoting Wholesale Competition Through Open AccessNondiscriminatory Transmission Services by Public Utilities,” requiredjurisdictional public utilities to file open access transmission tariffsto allow competition in the supply of wholesale electrical energy. Underthe Order 888 market entities (utilities, merchant generators, energytraders, etc) compete to provide energy based on several factorsincluding cost and availability of transfer capacity on transmissionfacilities. Market entities can be limited from providing energy tocertain regions based on the availability of transfer capacity ontransmission facilities. This order had the effect of introducingcompetition by allowing access to the transmission system to allowtransportation of electricity from buyer to seller.

[0005] A next stage in the development of electricity markets was theFERC Order 2000, “Regional Transmission Organizations,” issued inDecember 1999. This order required jurisdictional public utilities toform and participate in a Regional Transmission Organization (“RTO”).The operational control of generators, and transmission facilities wasassigned to the Regional Transmission Organization. Under FERCregulations, RTOs are required, among other things; to ensure that itstransmission customers have access to an ancillary services and realtime balancing market. An RTO may cover parts of one or more stateswithin the United States. RTOs are required to maintain efficienttraffic grid management, to improve grid reliability, to monitor andmitigate against opportunities for discriminatory transmissionpractices, and to improve competition in the wholesale electricitymarkets. The RTO is expected to administer the open access transmissiontariff, to exercise operational control over congestion management,reliability and to plan the expansion of its transmission system. Anadditional set of requirements for RTOs are that they remain independentof the market participants.

[0006] FERC also authorized the startup of several regional electricitymarkets, including the PJM, ISO NE, NYISO, and the CAISO. These marketshad different rules including those that govern a wholesale spot marketfor electrical energy. The operators of these markets are faced with theneed to select offers provided by market participants that satisfyrequirements and operating constraints.

[0007] The next stage in the development of electricity markets is theJuly 2002, FERC Notice of Proposed Rulemaking (NOPR), “Remedying UndueDiscrimination through Open Access Transmission Service and StandardElectricity Market Design.” This NOPR announces FERC's intent to form astandard market design for wholesale electrical energy that would applyto all jurisdictional utilities This NOPR requires public utilities toplace their transmission assets that are used in interstate commerceunder the control of an Independent Transmission Provider or ITP. Amongother functions, an ITP is responsible for operating a day ahead marketand a real time market for electrical energy and ancillary services.

[0008] In the day ahead market for electricity, spot market prices aregenerally determined based on offers to supply energy and on forecastrequirements for load. One possible solution is to determine a supplycurve using either marginal costs or bid prices to rank order the plantsbeginning with the cheapest plants. Bids are selected starting with thecheapest and ascending until requirements are satisfied. However, it isnecessary to consider operational constraints, which leads to selectionof bids out of merit order. Heuristic methods are used to determinewhich bid to select out-of-order. There are, however, better possibleapproaches that are based on optimization. Additionally, the FERC NOPRrecognizes that to create a truly competitive wholesale power market,the market must also allow for price responsive loads.

[0009] In this framework, the market operator receives pricinginformation from various wholesale market generators (typicallycoal-fired power plants, hydroelectric power plants, nuclear powerplants, etc.) and receives energy requirements information from the LoadServing Entities The market operator is then responsible for determiningan operating plan based on the offers provided by the various marketgenerators and the bids provided by the various Load Serving Entities inthe most cost effective manner.

[0010] Optimization tools are necessary to determine market clearing andcommodity pricing based on submitted offers, while meeting operating andsecurity constraints. This invention addresses the needs of a marketoperator by allowing the modeling of the technical characteristics ofthe offers as well as the transmission operating and securityconstraints. Offers include the supply of ancillary services by means ofgenerating units and as well as price sensitive loads. The inventionallows the selection of the optimal choice among the offered productsbased on selected criteria such as minimizing the payments made by themarket operator to the market suppliers. The present invention addressthe above noted needs by facilitating an efficient day ahead clearanceand pricing mechanism for complex co-optimized solutions for trading ofenergy and ancillary services.

SUMMARY OF THE INVENTION

[0011] According to one aspect of the invention, there is provided asystem for optimizing the selection of offers submitted to the marketoperator by market participants such that all requirements for energyand ancillary services are satisfied along with operating and securityconstraints. The problem is formulated as a mixed integer linearprogram. Offers are formulated as piecewise linear functions. Operatingconstraints are formulated as linear inequalities. Commitment orselection decisions are formulated as integer variables. The results ofthis problem are the market clearing prices for each offered commodityand the amounts of products to be awarded to each market participant.

BRIEF DESCRIPTION OF THE FIGURES

[0012] The present invention will now be described with reference to theaccompanying drawings wherein:

[0013]FIG. 1 is a schematic diagram of the system in accordance with theprinciples of the present invention.

DETAILED DESCRIPTION OF THE FIGURES

[0014] To illustrate the principles of the present invention, a SecurityConstrained Unit Commitment (SCUC) co-optimization engine as developedby Siemens Power Transmission & Distribution, Inc., the assignee of thepresent invention, shall be described in detail. While this SCUCco-optimization engine constitutes a preferred embodiment of theinvention, it is not the intention of applicants to limit the scope ofthe invention to the particular details of this engine. Rather, it isthe intention of the applicants that the invention be defined by theappended claims and all equivalents thereto.

[0015] Referring to FIG. 1, there is shown an exemplary block diagram ofthe components and interfaces of an SCUC co-optimization engine 100 inaccordance with the principles of the present invention. The SCUCco-optimization engine 100 consists generally of a Market User Interface102, a Load Forecast engine 104, a component for handling and archivingmarket data (HIS) 106, SCUC 108, a component for market commoditypricing (Pricing Engine) 110, and a Market Database 114. A Mixed IntegerLinear Programming engine is also included as an optimization tool(MILP), 118.

[0016] The objective of the day ahead security constrained unitcommitment problem is defined as a minimization of the sum of the totalmarket costs. This can be mathematically formulated as:${\sum\limits_{t = 1}^{T}\left\{ {\sum\limits_{i = 1}^{N}\left\lbrack {{{c_{start}\left( {i,t} \right)} \cdot {Z\left( {i,t} \right)}} + {{c_{nold}\left( {i,t} \right)} \cdot {Y\left( {i,t} \right)}} + {c_{en}\left( {i,t} \right)} + {c_{reg}\left( {i,t} \right)} + {\sum\limits_{j \in {com}^{\prime}}{c_{j}\left( {i,t} \right)}}} \right\rbrack} \right\}}->{Min}$

[0017] where:

[0018] c_(start)(i,t) is the start up cost of the generating bid i attime step t;

[0019] Z(i,t) is the start up binary variable of the generating bid i intime step t;

[0020] c_(mold) (i,t) is the no load cost segment of the generating bidi in time step t;

[0021] Y(i,t) is the status binary variable of the generating bid i intime step t;

[0022] c_(en) (i,t) is the cost of the commodity energy of the bid i intime step t;

[0023] c_(reg) (i,t) is the cost of the commodity regulating reserveenergy of bid I in time step t;

[0024] The above formulation assumes that in a most general case the dayahead SCUC is a large co-optimization problem. The co-optimizationproblem simultaneously clears energy, regulation and other ancillaryservices, mainly reserves. In the above formulation, the assumption isthat three types of reserves can be supported. The three types ofreserves are (1) the ten minute spinning reserve, (2) the ten minutenon-spinning reserve, and (3) the thirty minutes operating reserve.

[0025] The total sum of the supply energy bids must be equal to the sumof load bids of price sensitive loads and load bids of pricenon-sensitive (fixed) loads for each time step of the study period. Themathematical formulation is:${{{\sum\limits_{i = 1}^{N}\frac{p_{en}\left( {i,t} \right)}{{pf}_{en}}} - {\sum\limits_{j = 1}^{N_{psld}}\frac{p_{psld}\left( {j,t} \right)}{{pf}_{ld}\left( {j,t} \right)}}} = {\sum\limits_{k = 1}^{N_{fxld}}{p_{fxld}\left( {k,t} \right)}}},{\forall t}$

[0026] where:

[0027] p_(en) (i,t) is the power of commodity energy of the bid I attime step t;

[0028] pf_(en) is the power penalty factor pf the generating bid I attime step t;

[0029] p_(psld) (i, ^(t)) is the power of price sensitive load of theload bid i at time step t;

[0030] pf_(ld) (i, t) is the power penalty factor of the price dependentload bid i at time step t;

[0031] p_(fxld) (i, t) is the power of price non-sensitive load of theload bid i at time step t;

[0032] The following ancillary services are considered in the presentmodel. The regulating reserve, ten minute spinning reserve, and thirtyminute operating reserve. The ancillary service constraints are (1)regulating reserve; (2) ten minute spinning reserve, (3) ten minutenon-spinning reserve, and (4) thirty minute operating reserve.

[0033] These ancillary services are considered in turn. The regulatingreserve must be greater than or equal to the system regulating reserverequirements, expressed mathematically as:${{\sum\limits_{i = 1}^{N}{p_{reg}\left( {i,t} \right)}} \geq {P_{reg}^{req}(t)}},{\forall t}$

[0034] where:

[0035] p_(reg)(i,t) is the power of commodity regulating reserve energyof the bid i at time t;

[0036] p_(reg) ^(req)(t) is the system regulating reserve requirementsat time step t.

[0037] and each regulating reserve bid must satisfy the followingrelations:

0≦p _(reg)(i,t)≦min{RR(i,t),ramp¹⁰(i),max[0,0.5·(RH(i,t)−SS∀i,t

[0038] where:

[0039] RR(i,t) is the regulating reserve range of the generating bid iat time step t;

[0040] RH(i,t) is the regulating high capacity limit of the generatingbid i at time step t;

[0041] SS(i,t) is the self committed and scheduled capacity of thegenerating bid i at time step t;

[0042] W(i,t) is the regulating status binary variable of the generatingbid i at time step t;

[0043] and ramp¹⁰(i) is the ten minute ramp capability of the generatingbid i.

[0044] For the ten minute spinning reserve, at each time step of thestudy period, the total ten minute spinning reserve must be greater thanor equal to the ten minute spinning reserve requirements, governed bythe following mathematical formulation:${{\sum\limits_{i = 1}^{N}{p_{tmsr}\left( {i,t} \right)}} \geq {P_{tmsr}^{req}(t)}},{\forall t}$

[0045] where:

[0046] p_(tmsr) (i,t) is the power of commodity ten minute spinningreserve of bid i at time step t;

[0047] and p_(tmsr) ^(req)(t) is the system ten minute spinning reserverequirement at time t.

[0048] Each ten minute spinning reserve bid must satisfy the followingmathematical formulation:

0≦p _(tmsr)(i,t)≦min[ramp ¹⁰(i,t),p _(max)(i,t)−SS(i,t)]·Y(i

[0049] As for the ten minute non-spinning reserve, at each time step ofthe study period, the ten minute non-spinning reserve must be greaterthan or equal to the system ten minute non spinning reserve requirementsby the following mathematical formulation:${\sum\limits_{i = 1}^{N}{p_{tmns}\left( {i,t} \right)}} \geq {{P_{tmns}^{req}(t)}\quad {\forall t}}$

[0050] where:

[0051] p_(tmns)(i,t) is the power of commodity ten minute non-spinningreserve of bid i at time step t;

[0052] and p_(tmns) ^(req)(t) is the system ten minute non-spinningreserve requirement at time t.

[0053] Each ten minute non-spinning reserve bid must satisfy thefollowing relation in mathematical formulation:

0≦p _(tmns)(i,t)≦min[ramp ¹⁰(i,t), p _(max)(i,t)−SS(i,t)]˜[1

[0054] As for the thirty minute operating reserve, at each time periodof the study period, the total thirty minute operating reserve must begreater than or equal to the system thirty minute operating reserverequirements, as governed by the following mathematical formulation:${\sum\limits_{i = 1}^{N}{p_{tmor}\left( {i,t} \right)}} \geq {{P_{tmor}^{req}(t)}\quad {\forall t}}$

[0055] where:

[0056] p_(tmor) (i,t) is the power of commodity ten minute operatingreserve of bid i at time step t;

[0057] and p_(tmor) ^(req)(t) is the system ten minute operating reserverequirement at time t.

[0058] Each thirty minute operating reserve bid must satisfy thefollowing relation:

0≦p _(tmor)(i,t)≦min[ramp ³⁰(i),p _(max)(i,t)−SS(i,t)]˜[1−Y(i,t)]∀i,t

[0059] Mixed integer linear programming techniques can be used to solvethis multivariate problem. Integer linear programming models can be usedwhere variables are constrained to take integer or whole number (asopposed to fractional) values. Mixed integer (MILP or MIP) problemsrequire only some of the variables to take integer values, whereas pureinteger (ILP or IP) problems require all variables to be integer.

[0060] In most energy markets, the bid cost curves for all commoditiessuch as energy, reserve, ten minute spinning reserve, etc. are definedas piecewise linear curves. One of the main factors impacting theperformance of the linear programming algorithms is the number of binaryinteger variables such as 0 and 1. If each segment of the piecewiselinear bid curves for various commodities is modeled as a separatevariable, the number of binary integer variables associated with thestatuses of units would be equal to the number of bids times the numberof segments of the corresponding piecewise linear bid curves.

[0061] Therefore, linear commodity bid cost curves are replaced with asingle linear term and a set of associated linear equations andvariables. Each piecewise linear commodity bid curve has a set of pairs(p_(com) ^(pl)(i,t,k),c_(com) ^(pl)(i,t,k)) of given vales associatedwith brake points k of piecewise linear bid cost curves. Since the bidcost curves c_(com)(i,t)=f(p_(com)(i,t)) are convex functions, thefollowing linear equations ensure that values of a single termc_(com)(i,t)=f(p_(com)(i,t)) remain always on the correspondingpiecewise linear curve:${p_{com}\left( {i,t} \right)} = {\sum\limits_{k}{{p_{com}^{pl}\left( {i,t,k} \right)} \cdot {\omega_{com}^{pl}\left( {i,t,k} \right)}}}$${c_{com}\left( {i,t} \right)} = {\sum\limits_{k}{{c_{com}^{pl}\left( {i,t,k} \right)} \cdot {\omega_{com}^{pl}\left( {i,t,k} \right)}}}$

[0062] subject to the following constraints:

0≦ω_(com) ^(pl)(i,t,k)≦1

[0063] and${\sum\limits_{k}{\omega_{com}^{pl}\left( {i,t,k} \right)}} = 1$

[0064] where ω_(com) ^(pl) (i,t,k) are weighting variables associated tothe piece-wise linear bid cost curve brake points. This enables modelingof each commodity costs with only one variable c_(com)(i,t) that followsthe convex piece-wise linear curve and that doesn't explicitly depend onbrake points and with additional variables ω_(com) ^(pl)(i,t,k) subjectto the same constraints. To ensure that the solution for c_(com)(i,t)follows the cost curves exactly under all circumstances (includingnon-convex curves), in the non-convex case the series ω_(com) ^(pl)(i,t, k) cannot have more than two adjacent non-zero elements in thedefining ordering of the series. In the general case the variablesω_(com) ^(pl)(i,t,k) have to form special order sets (“SOS”) modeledexplicitly by the linear programming engine of the CPLEX product.

[0065] The solution to the problem is constrained by the followingrestraints. The bid ramping constraint restricts the maximal up and downchanges of the bid's electrical generation between the two consecutivetime steps, expressed in the following mathematical constraint:

p _(en)(i,t)−p _(en)(i,t−1)≦ramp _(up) ^(max)(i,t) and

p _(en)(i,t−1)−p_(en)(i,t)≦rampd_(dn) ^(max)(i,t)

[0066] In another embodiment, the bid ramping constraint may need to bedefined per segment of energy bid cost curve.

[0067] Another constraint is the startup variable and status variableconstraints. The following constraints are imposed on start up variableZ(i,t):

Z(i,t−1)−Y(i,t)+Y(i,t−1)≧0

Z(i,t)+Y(i,t)≦1 and

Z(i,t−1)−Y(i,t)≦0

[0068] The following constraint is imposed on regulating statusvariable:

W(i,t)−Y(i,t)≦0

[0069] There are additionally minimum up and down time constraints. Thefollowing mathematical relationships are related to the constraints nthe bids minimum up and down times:

(Y(i,k+t+2)−Y(i,k+t+1))−(Y(i,t+1)−Y(i,t))≧−1

[0070] k=0, . . . ,MUT(i)−2,

[0071] t=0, . . . , t_(end)−k−2

(Y(i,k+t+2)−Y(i,k+t+1))−(Y(i,t+1)−Y(i,t))≦1

[0072] k=0, . . . ,MDT(i)−2,

[0073] t=1, . . . , t_(end)−k−2

[0074] Another restraint is the limit on bid powers, as definedmathematically as follows:

p _(en) (i,t)−0.5·p _(reg) (i,t)≧p_(min) (i,t)·Y(i,t)+[RL(i,t

and

p _(en) (i,t)+p _(reg) (i,t)+p _(tmsr)(i,t)+p _(tmnsr)(i,t)+p _(tmor) (

[0075] Another restraint is the transmission constraint. The linearconstraints that impose transmission constraints on line k as a functionof generating power of bid i are defined by:${{- {P_{\lim}^{t}\left( {k,t} \right)}} \leq {\sum\limits_{i = 1}^{N}{{{shf}\left( {k,i} \right)} \cdot {p_{en}\left( {i,t} \right)}}} \leq {{P_{\lim}^{t}\left( {k,t} \right)}\quad {\forall\quad k}}},t$

[0076] The above described embodiments are merely exemplary. Those ofordinary skill in the art may readily devise their own implementationsthat incorporate the principles of the present invention and fall withinthe spirit and scope thereof.

What is claimed is:
 1. A computer implemented system for optimal marketpricing of dispatched energy and ancillary services in an electricitymarket of at least one market participant wherein load prediction isperformed considering load system requirements, said system comprising:means for inputting transmission security constraints of said at leastone market participant; means for clearing energy and ancillary servicebids; and means for pricing the dispatch of energy and ancillaryservices considering said load security constraints of said at least onemarket participant using mixed integer linear programming techniques. 2.The market dispatch system of claim 1, wherein said load securityconstraint is the market participant energy limit.
 3. The marketdispatch system of claim 1, wherein said load security constraint is theload energy limit.
 4. The market dispatch system of claim 1, whereinsaid load security constraint is the market participant regulationavailability.
 5. The market dispatch system of claim 1, wherein saidload security constraint is the market participant regulation range. 6.The market dispatch system of claim 1, wherein said load securityconstraint is the market participant spinning reserve limit.
 7. Themarket dispatch system of claim 1, wherein said load security constraintis the load spinning reserve limit.
 8. The market dispatch system ofclaim 1, wherein said load security constraint is the market participantnon-spinning reserve limit.
 9. The market dispatch system of claim 1,wherein said load security constraint is the market participant capacitylimit.
 10. The market dispatch system of claim 1, wherein said loadsecurity constraint is the load capacity limit.